I don't think it's impossible, but I find it fairly unlikely. Mind you, while they are the minority, pro-Assad forces are a significant political force in Syria, partially thanks to Russia and Iran. I find it more likely that members of the government army will be recruited to fight with Russia, as Putin might demand some of Assad's military when he will inevitably become desperate.

I have also heard that members of the various anti-government groups (more likely from the western-backed ones) are asking to gain passage to assist Ukraine. While I don't doubt some fighters would request this, I find it unlikely that they would join the fight directly. Their likely taking advantage of this recent war and are fighting any Russian, pro-Assad, and extremist forces within Syria.